As NYPD commissioner under Mayor Rudolph W. Giuliani from 1994 to 1996, Mr. Bratton launched a department-wide application of CompStat, a data-derived policing approach originally devised in the New York City Transit Police Department, where Mr. Bratton earlier served as chief. CompStat uses mapping and statistical summaries of weekly crime reports to help law enforcement discover crime trends. During his tenure, crime in the city decreased significantly, leading other cities, including Chicago, Baltimore, Washington, D.C., San Francisco and Los Angeles, to adopt the system. Mr. Bratton served as chief of the LAPD from tk to 2009.

Mr. Bratton, who most recently ran his own police consulting group, returns to a city changed dramatically, thanks to almost two decades of low-crime. In 1990 the city experienced more than 2,300 murders. In 2012, there were 419. “This was one crazy city in the early 1990s,” Mr. Bratton told reporters last month. “This area down here was a no man’s land at the time. It did require assertive policing but it was done constitutionally and respectfully.”

With crime at new lows, many citizens have turned their attention to civil rights issues. Mayor-elect de Blasio’s platform included his opposition to the NYPD’s controversial stop-and-frisk tactics, that have disproportionately targeted black and Latino New Yorkers.

At a press conference Thursday, Mr. Bratton said he planned to continue applying technology and tactics to policing. “Mayor-elect de Blasio’s priorities are my priorities,” Mr. Bratton said. “This is the best police force in the nation, and we are going to ensure our men and women have the best technology, the most innovative tactics and the strong support of the communities they protect.”

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